Grade 8 Interpreting Unit Rates in Context: Unit Mastery Quiz with Full Solutions

Purpose and scope

This is a focused Grade 8 mastery quiz for the topic Interpreting Unit Rates in Context within Ratios, Rates and Proportions. It assesses whether a learner can explain what a unit rate means, choose the correct units, and use that meaning to compare and decide in real situations.

For broader assessment of the whole Unit Rates and Rate Interpretation unit, use the linked record [rea.m08.number.ratios-rates-proportions.unit-rates.unit-mastery-quiz]. For prerequisite repair on ratio structure or decimal computation, use the linked equivalent-ratios and decimal-operations quiz records rather than reteaching those topics here.

Quiz format

• 10 questions
• 20 marks total
• Recommended time: 25 to 35 minutes
• Calculator: optional unless your classroom policy says otherwise

Mastery threshold recommendation

• Mastery: 17/20 or better, with no more than one interpretation error
• Secure but not yet mastered: 14/20 to 16/20
• Needs review: 13/20 or below

Interpretation matters more than arithmetic alone. A student who computes correctly but repeatedly misstates what the answer means should not be considered to have full mastery.

Marking guide at a glance

Award marks for both:

• correct computation when needed
• correct interpretation in words with units

A bare number such as 3.5 without meaning like 3.5 dollars per kilogram is not full-credit evidence.

---

Questions

1. Juice price

A store sells 3 L of juice for $6.

a) Find the unit rate.
b) Explain what your answer means in this situation.

Marks: 2

2. Walking speed

Mina walks 12 km in 3 hours.

a) Find Mina's unit rate.
b) State the meaning of the unit rate using a complete sentence.

Marks: 2

3. Which label matches the rate?

A car travels 180 km in 2 hours.

Choose the best interpretation of the unit rate:

A. 90 hours for each kilometre
B. 90 km for each hour
C. 180 km for each hour
D. 2 km for each hour

Explain briefly.

Marks: 2

4. Better buy

Granola bars are sold in two packs:

• Pack A: 8 bars for $5.60
• Pack B: 12 bars for $7.20

Which is the better buy? Use unit rates and interpret your result.

Marks: 2

5. Water filling rate

A tap fills 15 L in 5 minutes.

a) Find the unit rate.
b) If someone says, "The tap fills 5 minutes per litre," explain whether that is correct.

Marks: 2

6. Reading pace

Sofia reads 45 pages in 30 minutes.

a) Find her reading rate in pages per minute.
b) Explain what the unit rate tells you about Sofia's reading.

Marks: 2

7. Choosing a plan

Two phone data plans are advertised:

• Plan A: 6 GB for $24
• Plan B: 10 GB for $35

Which plan gives more data for each dollar? Show the unit rate and interpret it.

Marks: 2

8. Spot the unreasonable interpretation

A runner's rate is 8 metres per second.

Which statement is correct?

A. The runner takes 8 seconds to run 1 metre.
B. The runner runs 1 metre every 8 seconds.
C. The runner runs 8 metres in 1 second.
D. The runner runs 8 seconds in 1 metre.

Explain why the other statements do not match the given unit rate.

Marks: 2

9. Cost comparison with different units

Rice is sold in two sizes:

• 2.5 kg for $8.25
• 4 kg for $12.40

Which bag is cheaper per kilogram? State the unit price and the better choice.

Marks: 2

10. Open response: interpreting before deciding

A cyclist travels 27 km in 1.5 hours. Another cyclist travels 36 km in 2 hours.

a) Find each cyclist's unit rate in km/h.
b) Are they travelling at the same speed?
c) Write one sentence comparing their rates in context.

Marks: 2

---

Full solutions and marking key

1. Juice price

$6 ÷ 3 = $2 per litre.

Answer:

• a) The unit rate is $2/L.
• b) This means 1 litre of juice costs $2.

Marking:

• 1 mark for $2/L
• 1 mark for a correct contextual sentence

2. Walking speed

12 ÷ 3 = 4

Answer:

• a) Mina's unit rate is 4 km/h.
• b) This means Mina walks 4 kilometres each hour.

Marking:

• 1 mark for 4 km/h
• 1 mark for correct interpretation

3. Which label matches the rate?

180 ÷ 2 = 90

So the unit rate is 90 km/h.

Answer: B

It means the car travels 90 kilometres for each 1 hour.

Why the others are wrong:

• A reverses the units
• C does not divide by 2 hours
• D gives the wrong value and wrong relationship

Marking:

• 1 mark for choosing B
• 1 mark for a valid explanation

4. Better buy

Pack A: $5.60 ÷ 8 = $0.70 per bar
Pack B: $7.20 ÷ 12 = $0.60 per bar

Answer: Pack B is the better buy.

It costs 60 cents per bar, while Pack A costs 70 cents per bar. Since the cost per 1 bar is lower, Pack B is better value.

Marking:

• 1 mark for correct unit rates or equivalent comparison
• 1 mark for correct decision with interpretation

5. Water filling rate

15 ÷ 5 = 3

Answer:

• a) The unit rate is 3 L/min.
• b) The statement "5 minutes per litre" is not correct for this situation. The tap fills 3 litres in 1 minute, not 1 litre in 5 minutes. The units and relationship have been reversed.

Note: minutes per litre could be found, but it would be 5 ÷ 15 = 1/3 minute per litre, not 5 minutes per litre.

Marking:

• 1 mark for 3 L/min
• 1 mark for identifying and explaining the reversal

6. Reading pace

45 ÷ 30 = 1.5

Answer:

• a) Sofia reads 1.5 pages per minute.
• b) This means in each minute, Sofia reads about 1.5 pages.

Marking:

• 1 mark for 1.5 pages/min
• 1 mark for interpretation in context

7. Choosing a plan

Plan A: 6 ÷ 24 = 0.25 GB per dollar
Plan B: 10 ÷ 35 ≈ 0.286 GB per dollar

Answer: Plan B gives more data for each dollar.

Interpretation:

• Plan A gives 0.25 GB for $1
• Plan B gives about 0.286 GB for $1

Since Plan B gives more gigabytes per dollar, it is the better value.

Marking:

• 1 mark for correct unit-rate work
• 1 mark for correct decision and interpretation

8. Spot the unreasonable interpretation

Answer: C

The rate 8 metres per second means 8 metres in 1 second.

Why the others are wrong:

• A says 8 seconds per metre, which reverses the units and meaning
• B says 1 metre every 8 seconds, which is far slower and also reversed
• D is not a meaningful rate statement because seconds are not something you "run"

Marking:

• 1 mark for choosing C
• 1 mark for explanation of mismatch in the others

9. Cost comparison with different units

First bag: $8.25 ÷ 2.5 = $3.30 per kg
Second bag: $12.40 ÷ 4 = $3.10 per kg

Answer: The 4 kg bag is cheaper.

Its unit price is $3.10 per kilogram, compared with $3.30 per kilogram for the 2.5 kg bag.

Marking:

• 1 mark for correct unit prices
• 1 mark for correct choice with interpretation

10. Open response: interpreting before deciding

First cyclist: 27 ÷ 1.5 = 18 km/h
Second cyclist: 36 ÷ 2 = 18 km/h

Answer:

• a) Each cyclist travels at 18 km/h.
• b) Yes, they are travelling at the same speed.
• c) A correct comparison sentence is: Both cyclists travel 18 kilometres each hour, so neither one is faster.

Marking:

• 1 mark for both unit rates correct
• 1 mark for correct comparison sentence or equivalent interpretation

---

Common errors this quiz is designed to reveal

1. Reversing the units

Example error: saying 5 minutes per litre instead of 3 litres per minute.

Repair: Ask, "What happens in 1 of the second quantity?" Then rewrite as quantity per 1.

2. Giving only a number, not a meaning

Example error: writing 0.70 instead of $0.70 per bar.

Repair: Require a sentence starting with: For every 1 ... or This means ...

3. Choosing the larger total instead of the better unit rate

Example error: choosing the larger package without comparing price per item.

Repair: Compare the same unit each time: per 1 bar, per 1 kilogram, per 1 dollar, or per 1 hour.

4. Confusing "more per dollar" with "less dollars per item"

These can both describe value, but the units must stay consistent.

Repair: Decide first what the question is asking: data per dollar, cost per item, distance per hour, or time per kilometre.

Use guidance

Use this record when the learning target is specifically interpreting unit rates in context. If a student misses several items because of weak decimal division rather than weak interpretation, route them to [rea.m08.number.decimals-and-percents.decimal-operations.unit-mastery-quiz]. If the issue is setting up equivalent comparisons before finding a unit rate, route them to [rea.m08.number.ratios-rates-proportions.equivalent-ratios.unit-mastery-quiz].